Question

sin power 4 theta minus Cos power 4 theta is equal to sin square theta minus cos square theta

Answer 1

this is so easy........

Answer 2

Answer and Explanation:

To show : $\sin^4\theta-\cos^4\theta=\sin^2\theta-\cos^2\theta$

Solution :

Taking LHS,

$LHS=\sin^4\theta-\cos^4\theta$

$=(\sin^2\theta)^2-(\cos^2\theta)^2$

Apply property, $a^2-b^2=(a+b)(a-b)$

$=(\sin^2\theta-\cos^2\theta)(\sin^2\theta+\cos^2\theta)$

We know, $\sin^2\theta+\cos^2\theta=1$

$=(\sin^2\theta-\cos^2\theta)(1)$

$=\sin^2\theta-\cos^2\theta$

$=RHS$

So, LHS=RHS.